Nancy Pelosi, the House of Representatives minority leader, said she was confident President Obama’s landmark deal would not be halted by Congress.
Photograph: AGF/Rex Shutterstock

Barack Obama has enough votes to get the Iran deal through the House of Representatives, despite Republican efforts to block the historic nuclear accord, the minority leader, Nancy Pelosi, has said.

With a Senate vote looking increasingly secure for the president, Pelosi’s comments suggest it is now extremely unlikely that Congress will halt the deal.

Pelosi, the Democratic leader in the House of Representatives, said on Thursday in an interview with the Associated Press that she was confident House Democrats would have the votes if necessary to see the Iran deal through.

Her comments coincide with growing momentum among Democrats in favor of the agreement, struck by Iran and six world powers in July, despite a couple of high-profile defections.

On Wednesday, Joe Donnelly became the 24th Democrat in the Senate to publicly back the deal – a key gain for the Obama administration, given the Indiana senator ranks among the chamber’s most conservative Democrats and faces a tough re-election battle in 2018.

“Despite having questions about Iran’s intentions, I am willing to give this agreement the opportunity to succeed,” Donnelly said in a statement. “While I share the concerns expressed by the agreement’s critics about what may happen 10, 15, or 20 years from now, I cannot in good conscience take action that would shift the potential risks of 2026 and 2031 to 2016.”

Donnelly’s endorsement came despite an Associated Press report which disclosed that Iran will be allowed to use its own inspectors to investigate its Parchin nuclear site, where it has been alleged that Iran has worked to develop nuclear arms.

Just two Democrats in the Senate – New York senator Chuck Schumer and New Jersey senator Bob Menendez – have defied Obama by publicly rejecting the deal. Both senators have strong ties to the American Israel Public Affairs Committee, the influential organization that is leading the opposition to the agreement, and were expected to oppose it.

Congress is poised to vote on a resolution in September that would disapprove of the P5+1 agreement, which seeks to prevent Iran from obtaining a nuclear weapon.

Republicans, who control both chambers of Congress, are almost uniformly opposed to the deal and expect to garner enough votes to pass the resolution of disapproval.

But they would need at least 13 Democrats in the Senate and 44 Democrats in the House to join them in order to override a presidential veto, and Obama has declared in no uncertain terms that he will employ his veto pen against any attempts to kill the landmark deal.

Although the arithmetic appears to be on the president’s side, a substantial number of Democrats have yet to publicly endorse the deal and lobbying is expected to intensify on both sides of the debate when lawmakers return to Washington from a five-week recess. Republicans have conceded it is unlikely that enough Democrats will be persuaded to override their own president’s veto, but Obama is taking nothing for granted.

The president has continued to personally lobby members of his party who remain undecided on the deal in the midst of his vacation on Martha’s Vineyard. A White House official told the New York Times that Obama, in private phone calls, has appealed to Democratic lawmakers to make it clear if they support the accord and raise any concerns with his administration if they are still on the fence.

Democrats in Congress have not revealed any formal whip counts, and members can always change their mind amid pressure from the pro-Israel lobby.

The Israeli prime minister, Binyamin Netanyahu, is vehemently opposed to the deal and is relying on Ron Dermer, Israel’s ambassador to the US, to influence members of Congress against it.

Just 12 of the House’s 188 Democrats have publicly rejected the deal, largely placing attention on the Senate. Democrats in that chamber are “still a long way from being able to sustain a veto or stop the resolution [of disapproval] in the Senate”, a leadership aide told the Guardian.

Correction, 21 August 2015: This article originally said that Joe Donnelly faced re-election in 2016. That should have been 2018. That has been corrected.